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A broader context for monotonically monolithic spaces

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Abstract

This is a sequel of the work done on (strongly) monotonically monolithic spaces and their generalizations. We introduce the notion of monotonically κ-monolithic space for any infinite cardinal κ and present the relevant results. We show, among other things, that any σ-product of monotonically κ-monolithic spaces is monotonically κ-monolithic for any infinite cardinal κ; besides, it is consistent that any strongly monotonically ω-monolithic space with caliber ω 1 is second countable. We also study (strong) monotone κ-monolithicity in linearly ordered spaces and subspaces of ordinals.

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References

  1. A. V. Arhangel’skii, Continuous mappings, factorization theorems and function spaces, Trudy Mosk. Mat. Obsch., 47 (1984), 3–21 (in Russian).

    MathSciNet  Google Scholar 

  2. A. V. Arhangel’skii, Topological Function Spaces, Kluwer Acad. Publ. (Dordrecht, 1992).

    Google Scholar 

  3. A. V. Arhangel’skii, D-spaces and finite unions, Proc. Amer. Math. Soc., 132 (2004), 2163–2170.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. V. Arhangel’skii and R. Buzyakova, Addition theorems and D-spaces, Comment. Math. Univ. Carolinae, 43 (2002), 653–663.

    MATH  MathSciNet  Google Scholar 

  5. H. Bennett, A note on point-countability in linearly ordered spaces, Proc. Amer. Math. Soc., 28 (1971), 598–606.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Buzyakova, On D-property of strong Σ-spaces, Comment. Math. Univ. Carolinae, 43 (2002), 493–495.

    MATH  MathSciNet  Google Scholar 

  7. R. Buzyakova, Hereditary D-property of function spaces over compacta, Proc. Amer. Math. Soc., 132 (2004), 3433–Ű3439.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Engelking, General Topology, PWN (Warszawa, 1977).

    MATH  Google Scholar 

  9. G. Gruenhage, A note on D-spaces, Topology Appl., 153 (2006), 2229–2240.

    Article  MATH  MathSciNet  Google Scholar 

  10. I. Juhász, Cardinal Functions in Topology — Ten Years Later, Mathematical Centre Tracts, 123 (Amsterdam, 1980).

  11. O. G. Okunev, On function spaces with the topology of pointwise convergence: Hewitt extension and τ-continuous functions, Vestnik MGU, Matem., Mech., 4 (1985), 78–80 (in Russian).

    MathSciNet  Google Scholar 

  12. S. Purisch, Scattered compactifications and the orderability of scattered spaces. II, Proc. Amer. Math. Soc., 95 (1985), 636–640.

    Article  MATH  MathSciNet  Google Scholar 

  13. E. A. Reznichenko, A pseudocompact space in which only subsets of incomplete cardinality are not closed and discrete, Vestnik Mosk. Univ., 44 (1989), 69–70 (in Russian).

    MathSciNet  Google Scholar 

  14. V. V. Tkachuk, Monolithic spaces and D-spaces revisited, Topology Appl., 156 (2009), 840–846.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05311-970, São Paulo, Brasil

    O. T. Alas

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186, Col. Vicentina, Iztapalapa, C.P. 09340, México, D.F., México

    V. V. Tkachuk & R. G. Wilson

Authors
  1. O. T. Alas
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  2. V. V. Tkachuk
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  3. R. G. Wilson
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Correspondence to O. T. Alas.

Additional information

Research supported by Consejo Nacional de Ciencia y Tecnología de México, Grant U48602-F.

Research supported by Programa Integral de Fortalecimiento Institucional (PIFI), Grant 34536-55.

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Alas, O.T., Tkachuk, V.V. & Wilson, R.G. A broader context for monotonically monolithic spaces. Acta Math Hung 125, 369–385 (2009). https://doi.org/10.1007/s10474-009-9034-9

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  • DOI: https://doi.org/10.1007/s10474-009-9034-9

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